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166 records · Page 10

Dynamical evolution in the D1D5 CFT

It is interesting to ask: how does the radial space direction emerge from the CFT in gauge-gravity duality? In this context we resolve a long-standing puzzle with the gravity duals of two classes of states in the D1D5 CFT. For each class the CFT states are in the untwisted sector, suggesting that the energy gap should be 1/R y where R y is the radius of the circle on which the D1D5 CFT is compactified. For one class of states, the gravity dual indeed has exactly this gap, while for the other class, the gravity dual has a very deep throat, leading to an energy gap much smaller than 1/R y . We resolve this puzzle by showing that for the latter class of states, perturbing the CFT off its free point leads to the formation of a band structure in the CFT. We also explain why such a band structure does not arise for the first class of states. Thus for the case where a deep throat emerges in the gravity description, the dynamics of falling down this throat is described in the CFT as a sequential ‘hopping’ between states all of which have the same energy at the free point; this hopping amplitude converts an integer spaced spectrum into a closely spaced band of energy levels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modular flow in JT gravity and entanglement wedge reconstruction

It has been shown in recent works that JT gravity with matter with two boundaries has a type II ∞ algebra on each side. As the bulk spacetime between the two boundaries fluctuates in quantum nature, we can only define the entanglement wedge for each side in a pure algebraic sense. As we take the semiclassical limit, we will have a fixed long wormhole spacetime for a generic partially entangled thermal state (PETS), which is prepared by inserting heavy operators on the Euclidean path integral. Under this limit, with appropriate assumptions of the matter theory, geometric notions of the causal wedge and entanglement wedge emerge in this background. In particular, the causal wedge is manifestly nested in the entanglement wedge. Different PETS are orthogonal to each other, and thus the Hilbert space has a direct sum structure over sub-Hilbert spaces labeled by different Euclidean geometries. The full algebra for both sides is decomposed accordingly. From the algebra viewpoint, the causal wedge is dual to an emergent type III 1 subalgebra, which is generated by boundary light operators. To reconstruct the entanglement wedge, we consider the modular flow in a generic PETS for each boundary. We show that the modular flow acts locally and is the boost transformation around the global RT surface in the semiclassical limit. It follows that we can extend the causal wedge algebra to a larger type III 1 algebra corresponding to the entanglement wedge. Within each sub-Hilbert space, the original type II ∞ reduces to type III 1 .

2D Gravity↗

Universal CMB 𝐵-mode spectrum from early causal tensor sources

Many early Universe scenarios predict postinflationary tensor perturbations from causality-limited, subhorizon sources. While the microphysical details may be different, as long as these sources are bounded in duration and correlation length, their tensor power spectra exhibit a universal scaling behavior at small wave number: 𝒫 ℎ ⁡(𝑘)∝𝑘 3 , corresponding to white noise on superhorizon scales at the time of production. If these early causal tensor sources (ECTs) exclusively produce gravitational waves before redshift 𝑧 ∼10 5 , this scaling is realized on all of the scales observed in the CMB, and thus yields a universal multipole distribution for the 𝐵-mode angular power spectrum. Unlike the scale-invariant distributions of inflationary 𝐵 modes, ECTs generically predict enhanced power on small scales and suppressed power on large scales, which allows these source classes to be distinguished given measurements over a sufficient range of angular scales. In this paper, we introduce a unified framework for characterizing ECTs and demonstrate how their universal infrared scaling manifests in low-frequency observables, including CMB 𝐵 modes and stochastic gravitational wave spectral densities. We illustrate this mapping with representative case studies of this universality class involving first-order phase transitions, topological defects, and enhanced scalar perturbations, which source tensor modes at second order in perturbation theory.

79 ASTRONOMY AND ASTROPHYSICS↗

Foldable Instrumented Bits for Ultrasonic/Sonic Penetrators

Long tool bits are undergoing development that can be stowed compactly until used as rock- or ground-penetrating probes actuated by ultrasonic/sonic mechanisms. These bits are designed to be folded or rolled into compact form for transport to exploration sites, where they are to be connected to their ultrasonic/ sonic actuation mechanisms and unfolded or unrolled to their full lengths for penetrating ground or rock to relatively large depths. These bits can be designed to acquire rock or soil samples and/or to be equipped with sensors for measuring properties of rock or soil in situ. These bits can also be designed to be withdrawn from the ground, restowed, and transported for reuse at different exploration sites. Apparatuses based on the concept of a probe actuated by an ultrasonic/sonic mechanism have been described in numerous prior NASA Tech Briefs articles, the most recent and relevant being "Ultrasonic/ Sonic Impacting Penetrators" (NPO-41666) NASA Tech Briefs, Vol. 32, No. 4 (April 2008), page 58. All of those apparatuses are variations on the basic theme of the earliest ones, denoted ultrasonic/sonic drill corers (USDCs). To recapitulate: An apparatus of this type includes a lightweight, low-power, piezoelectrically driven actuator in which ultrasonic and sonic vibrations are generated and coupled to a tool bit. The combination of ultrasonic and sonic vibrations gives rise to a hammering action (and a resulting chiseling action at the tip of the tool bit) that is more effective for drilling than is the microhammering action of ultrasonic vibrations alone. The hammering and chiseling actions are so effective that the size of the axial force needed to make the tool bit advance into soil, rock, or another material of interest is much smaller than in ordinary twist drilling, ordinary hammering, or ordinary steady pushing. Examples of properties that could be measured by use of an instrumented tool bit include electrical conductivity, permittivity, magnetic field, magnetic permeability, temperature, and any other properties that can be measured by fiber-optic sensors. The problem of instrumenting a probe of this type is simplified, relative to the problem of attaching electrodes in a rotating drill bit, in two ways: (1) Unlike a rotating drill bit, a bit of this type does not have flutes, which would compound the problem of ensuring contact between sensors and the side wall of a hole; and (2) there is no need for slip rings for electrical contact between sensor electronic circuitry and external circuitry because, unlike a rotating drill, a tool bit of this type is not rotated continuously during operation. One design for a tool bit of the present type is a segmented bit with a segmented, hinged support structure (see figure). The bit and its ultrasonic/sonic actuator are supported by a slider/guiding fixture, and its displacement and preload are controlled by a motor. For deployment from the folded configuration, a spring-loaded mechanism rotates the lower segment about the hinges, causing the lower segment to become axially aligned with the upper segment. A latching mechanism then locks the segments of the bit and the corresponding segments of the slider/guiding fixture. Then the entire resulting assembly is maneuvered into position for drilling into the ground. Another design provides for a bit comprising multiple tubular segments with an inner alignment string, similar to a foldable tent pole comprising multiple tubular segments with an inner elastic cable connecting the two ends. At the beginning of deployment, all segments except the first (lowermost) one remain folded, and the ultrasonic/sonic actuator is clamped to the top of the lowermost segment and used to drive this segment into the ground. When the first segment has penetrated to a specified depth, the second segment is connected to the upper end of the first segment to form a longer rigid tubular bit and the actuator is moved to the upper end of the second segnt. The process as described thus far is repeated, adding segments until the desired depth of penetration has been attained. Yet other designs provide for bits in the form of bistable circular- or rectangular- cross-section tubes that can be stowed compactly like rolls of flat tape and become rigidified upon extension to full length, in a manner partly similar to that of a common steel tape measure. Albeit not marketed for use in tool bits, a bistable reeled composite product that transforms itself from a flat coil to a rigid tube of circular cross section when unrolled, is commercially available under the trade name RolaTube(TradeMark) and serves as a model for the further development of tool bits of this subtype.

Bar-Cohen, Yoseph↗